Method and system of efficient spectrum utilization by communications satellites

ABSTRACT

A satellite system includes a plurality of orbit slots having a first orbital and a second orbital slot. A first satellite occupies a first orbital slot and generates a first set of uniform beams. A second satellite located in a second orbital slot generates a second set of uniform beams. A tiling pattern on the face of the Earth has a plurality of cells, with each of the cells having a defined frequency for communication. The first set of beams and the second set of beams are generated according to parameters to avoid interference between them. The parameters may include satellite orbit separations, beam size, multiplicity of band reuse, and ground station received beamwidth.

CROSS-REFERENCE TO RELATED APPLICATION

The present application is a continuation of prior application Ser. No.09/664,940, filed Sep. 19, 2000 now U.S. Pat. No. 6,810,249, entitled“Method and System of Efficient Spectrum Utilization by CommunicationsSatellites”, inventors: Thomas M. Walsh, George Hrycenko, William J.Nunan and Adam Stone, the entire contents of which are incorporatedherein by this reference.

TECHNICAL FIELD

The present invention relates to communications satellites, and moreparticularly, to a coordinated system for satellite networks used toimprove frequency reuse.

BACKGROUND ART

Satellites in geostationary orbit (GSO) have been widely preferred forseveral decades because of economic advantages. In a geostationaryorbit, a satellite traveling above the Earth's equator, in the samedirection as that in which the Earth is rotating, and at the sameangular velocity, appears stationary relative to a point on the Earth.These satellites are always “in view” at all locations within theirservice areas. Antennas on Earth need to be aimed at a GSO satelliteonly once; no tracking system is required.

Coordination between GSO satellites generally occurs on a first-come,first-served, basis; such coordination sometimes is facilitated bygovernmental allocation of designated “slots” angularly spaced accordingto service type.

Given the desirability of geostationary satellite orbits and technicallimits in spacecraft and earth station design, the number of satellitesthat can effectively serve a given area on the earth using a particularband of operation (e.g., “C-band”, or “Ku-band”) is limited. Whileefforts have continued to improve the technology to enhance capacity,governments have on occasion resorted to auctions as a mechanism toassign limited orbital resources where the demand has exceeded theapparent supply. These circumstances have encouraged the development ofcomplex and expensive new systems including those using low Earth orbit(LEO), medium Earth orbit (MEO), and higher frequencies, for example,the Ka band (up to approximately 40 GHz). Growth to higher frequenciesis limited by problems of technology and propagation: thus some effortsat expanding satellite applications involve exploitation of the spatialdimension (i.e., utilizing satellite orbits other than the GSO). A hostof proposed LEO and MEO systems exemplify this direction.

The recently filed LEO and MEO system applications, however, introduceadditional technical complexity and costs that may not be justified insome applications. Frequency coordination and sharing are complicated bythe unstructured crisscrossing of the lines of sight of these systems.

In the use of geostationary orbits, objectives in establishing networksis to maximize the independence between satellites. To achieve this, theburden of coordination is placed on the later entrant, to ensureinterference-free operation vis-à-vis existing systems. Because of thenumber of networks in operation, particularly in the heavily utilizedC-band and Ku-band, interference-free capacity is very difficult (if notimpossible) to coordinate for service areas including the populated landmasses. It would therefore be desirable to provide a system forcoordinating various satellite operations so that the aggregatecommunications capacity of all satellites may be improved, and theoverall utilization of the resource is increased. It would therefore bedesirable to provide a system for coordinating various satelliteoperations so that the aggregate communications capacity of satellitesmay be maximized.

SUMMARY OF THE INVENTION

An object of the present invention is to provide a method for maximizingthe aggregate capability of geosynchronous communications satellites foraccommodating a multiplicity of services and/or providers.

Another object is to enable frequency reuse of spectrum used bygeosynchronous satellites in an optimally coordinated manner, accountingfor maximum number of requirements within a given band and geographicalregion.

A typical example of the invention, a satellite system has a pluralityof orbit slots having a first orbital slot and a second orbital slot. Afirst satellite occupies a first orbital slot and generates a first setof beams. A second satellite in a second orbital slot generates a secondset of beams. A tiling pattern results in a plurality of cells on theface of the Earth that defines all coverage areas to be served by theplurality of satellites. The beams of each satellite cover cells withinits field of view that represent a subset of the overall tiling pattern.Each of the cells has a defined frequency sub-band for communication andis covered by a beam. The tiling pattern is generated in a way thatallows frequency reuse, provides contiguous coverage, and minimizesinterference between the all satellites. The key parameters indetermining interference and reuse are cell size and the relatedbeamwidth, satellite arc spacing along with the related Earth stationbeamwidth, and the frequency reuse scheme. Other embodiments of thisconcept include more than two orbital positions (or “slots”).

Other objects and features of the present invention will become apparentwhen viewed in light of the detailed description of the preferredembodiment when taken in conjunction with the attached drawings andappended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a map showing geostationary satellites in equally-spacedorbits on a portion of the GSO arc.

FIG. 2A is a perspective view of a plurality of GSO satellitespositioned above the Earth, and projecting beams upon the surface of theEarth, according to the single tiling pattern.

FIG. 2B is an enlarged view of a cell and the associated beam accordingto the present invention showing that cells provide contiguous coverage.

FIG. 3 is a map showing one embodiment of a tiling pattern thataccommodates 0.5° beams.

FIG. 4 is a map showing the tiling patterns that omits cells over theoceans.

FIG. 5 is a histogram showing the number of cells of FIG. 4 that can beutilized from the given number of orbit slots, assuming an elevationangle of greater than 20°, and slots spaced 6° apart from −30° to +150°longitude.

FIG. 6 is a graphical representation of a tiling pattern from theperspective of a satellite and the associated frequencies resulting froma scheme that has 3 sub-bands.

FIG. 7 is a graphical representation of a tiling pattern demonstrating areuse scheme that uses four sub-bands.

FIG. 8 is a graphical representation of a tiling pattern using a reusescheme that uses seven sub-bands.

FIG. 9 is a plot of the accessible portion of the GSO arc versus celllatitude for three different Earth station elevation angles.

FIG. 10 is a map showing an alternative tiling pattern for 2° beams.

BEST MODE(S) FOR CARRYING OUT THE INVENTION

The present invention is illustrated herein in terms of a system ofsatellites distributed along a portion of the GSO arc using a tilingpattern covering a portion of the Earth. However, it is to be understoodthat the invention may also be used with non-GSO satellites. Also, theinvention could ultimately be applied to all future GSO satellites.Thus, as GSO satellites are replaced, the teachings of the presentinvention may be employed to promote frequency reuse and coordinatedoperation with the replacement satellites.

The essence of this invention is the establishment of relationshipsbetween satellites to maximize spectrum and orbit utilization. Theserelationships are particularly applicable to the “Fixed SatelliteService” and the “Broadcasting Satellite Service” as defined in theRadio Regulations of the International Telecommunications Union;however, other satellite services may employ these concepts. Asdescribed below, optimum relationships are defined in terms of the keyparameters of orbit arc separation, earth station and space stationantenna beamwidths, and earth cell coverage dimensions, that results inmaximization of overall communications capacity.

This concept is developed under the cooperative constraints of bandsegmentation, band reuse, a specification of maximum satellite antennasize, specification of minimum earth terminal antenna size, and a givenminimum relative signal strength in the presence of noise andinterference that is required for acceptable communication ofinformation in the band. The relative signal strength is commonlydenoted C/(N+I), and represents the intended signal power (C) divided bythe sum of noise power due to various natural thermal processes (N) andpower due to all interfering signals (I) occupying the same frequencyband as the intended signal.

All satellites within a given orbital arc operating in the subjectfrequency band will operate subject to the condition of having similarperformance parameters. Enforcing a near uniform signal power, and auniform C/(N+I) requirement for all beams sharing a band leads to ahigher overall communication capacity than can be realized otherwise.

Decreasing the extent of geographical overlap between beams sharing thesame or adjacent spectral assignments (i.e., decreasing the signal leveloutside the intended service area) reduces interference between thesystems (networks). Minimizing the size and maximizing the number ofbeams serving a given region increases the frequency re-use andconsequently the overall communication capacity to be derived from agiven band. One attractive method of satisfying these competingobjectives of minimizing interference while maximizing overall capacityis use of a repeating, geometrical arrangement of cells in which thecell coverage areas may be said to “tile” the geographic area to whichsatellites provide communication service. This arrangement of cellsdefines the tiling pattern. Each of the plurality of beams of asatellite is designed to cover a particular cell of the tiling pattern.

This frequency re-use scheme has been previously applied to individualsatellites. In this invention, the frequency re-use scheme is extendedto apply to a number of satellites in a coordinated system. Thedifference in the present invention is that the compatibility betweenall satellites and their respective earth terminals is a-priori builtinto the coordinated system of communications satellites where allsatellites of participating networks can operate above an acceptable(N+I) threshold.

An increase in satellite antenna size makes possible a decrease in thesize of beam that it can produce, and a single antenna can produce manybeams. The diameter of the antenna is dictated by the size of thesmallest beam, and not by the number of beams it must produce. Thus,larger satellite antennas (although typically more expensive thansmaller ones) decrease beam size and increase aggregate communicationscapacity.

Similarly, an increase in earth terminal antenna size decreases therequired separation distance between satellites using the same frequencyband. This separation distance can be quantified as a GSO slot spacing,which is the difference in longitude of two adjacent geostationary orbitpositions.

By selecting the earth station antenna size to minimize possibleadjacent satellite interference, it is possible to re-use the fullspectrum from each GSO slot; therefore, the smaller the GSO slotspacing, the more usable GSO slots exist, and the greater the overallcommunication capacity.

The present invention does not attempt to define the best size forantennas of satellites or earth terminals. Likewise, it does not attemptto define a unique best value for C/(N+I). These choices entail economicjudgments regarding the relative value of overall capacity or reducedprobability of data transmission errors. Instead, this invention showshow to maximize the overall communication capacity of the coordinatedsystem for any specified values of satellite beam size and GSO slotspacing, while achieving a specified value of C/(N+I).

For a given choice of antenna sizes, this frequency assignment methodgenerates a set of frequency reuse schemes, the first three of which areillustrated in FIGS. 6 through 8. The reuse scheme defines the number ofdistinct sub-bands into which the available frequency band is divided,and how those sub-bands are assigned to the various cells covering theregion. Each figure illustrates a particular reuse scheme, for which thenumber of sub-bands is three, four, and seven respectively. Increasingthe number of sub-bands increases CI(N+I), but decreases thecommunication bandwidth to each cell or it can be used to reduce theantenna size.

C/(N+I) also depends on the proper match of beam size to cell size,where beams are characterized by antenna patterns. Antenna patternsmathematically describe the degree to which the power radiated by anantenna varies over the field of view of the antenna as a function ofangle. Typically, the power radiated is maximum at the center of thebeam, and decreases in proportion to the square of the angular distancefrom the center over a restricted radius of the main beam.

The beamwidth is typically defined as the angular distance betweenpoints on the antenna pattern at which the power falls to one half ofits peak value.

In a region of the antenna pattern that is well beyond

$»\frac{3}{4}q\; 3\mspace{14mu}{dB}$off beam peak, the half-power beamwidth, there is a distribution ofrapid power variations as a function of angle, known as “sidelobes”;these features of realistic antenna patterns also influence theachievable C/(N+I).

Within each beam there is a region to which that beam provides service,and which is referred to as a service area. Outside the service area isa region into which the beam projects significant amounts of radiofrequency power, but in which the beam cannot guarantee service at orabove the minimum specified C/(N+I). Thus, power which a given beamdeposits outside its target cell (or service area) is a loss and cancontribute to interference power (I) in neighboring cells.

The choice of optimum cell size for a given beam size involves atrade-off: increasing the cell size relative to the beam diameterreduces the interference power that a beam generates in neighboringcells, and likewise reduces the interference that those neighboringcells generate in the cell in question. This is an advantage forcommunication at or near the center of the cell; however, every pointwithin each cell must receive the intended signal at or above thespecified C/(N+I). At the periphery of a cell that is larger than thehalf-power beamwidth, the intended signal power (C) is less than halfthat at the center. Changing the cell size relative to the givenhalf-power beamwidth therefore varies both the signal strength and theinterference.

For each reuse scheme and antenna pattern combination, there exists acell size relative to a desired beam size that maximizes C/(N+I). Therequirements of the quality of communication service to which thisassignment method is being applied will determine which of the availablereuse schemes is most appropriate, depending on the relative importanceof the width of the sub-bands versus achievable C/(N+I).

A key feature of this invention is that each defined beam can be assuredof providing its intended coverage area (cell) service at or above thespecified C/(N+I), regardless of whether none, some, or all of the otherbeams in the coordinated system are active, provided that any activebeams do not exceed their constraints on size, position, or power perunit frequency. Other factors include earth station sides and thebeamwidth and satellite spacing.

Referring now to FIGS. 1 and 2A, a map 10 shows a portion of the Earth,with possible geostationary satellite locations or slots 12, of thepresent invention, positioned with equal spacing over the equator. Theslots 12 provide one of the defined relationships of the presentinvention between satellites 24 covering the same geographic area.

A coordinatable system of the present invention, is generally indicatedby reference numeral 16. Coordinatable system 16 includes a firstsatellites 18 and a second satellites 20. Other satellites not belongingto the system of the present invention 22 may be located on GSO arc 14.As will be further described below, the operating parameters of thefirst satellite 18, and the second satellite 20, are coordinated by theuniformly defined relationships of the present invention. Othersatellites 22 may be accommodated at a loss of spectrum efficiency.First satellite 18 and second satellite 20 are generally represented byreference numeral 24.

Referring now to FIG. 2A, a plurality of GSO satellites 24 arepositioned at an altitude of over 35,000 kilometers above the Earth on aplane which intersects the equator, each covering the same geographicalarea.

A landmass 26 is shown having a tiling pattern 28 extending thereacross.Tiling pattern 28 may also extend across the entire surface of theEarth. Tiling pattern 28 is formed of a number of cells 30. Satellites24 generate beams 32. As the distance from the equator increases, thesize of cells 30 projected onto the Earth, increases to reflect thenatural tendency of GSO satellite spot-beam footprints to be largerfurther away from the equator in terms of earth surfaces that areintersected. This allows the satellites to be configured with antennaelements that generate uniform size beams.

One advantage of each satellite generating the same size beams allows anorbital spare to be positioned to replace any satellite that becomesinoperable in orbit.

Referring now to FIG. 2B, each cell 30 of the tiling pattern, thus,approximates the circular or elliptical beam patterns 32 generated bysatellites 24. Cell 30 is preferably a hexagon. A hexagon is preferredover another polygon such as a square, since a square has more spilloverthan a hexagon when a circle is circumscribed about its perimeter.

Referring now to FIG. 3, a complete tiling pattern 28 is illustratedextending across the continents of Africa, Europe and Asia using 0.5°beamwidths.

By cellularization of a service area, a high degree of spectrum reusemay be achieved. As illustrated, the coverage area is divided into a setof regular cells. The regular cells, as illustrated, are hexagonal inform. The hexagons intersection of the earth's surface vary in size overthe coverage area. That is, as latitude is increased, the size increasesproportionally.

One advantage of a hexagonal grid is that only three cells meet at eachvertex, rather than four as in a square grid. Each hexagonal celltouches only six neighboring cells while a square would touch eight. Thehexagonal cell structure has a higher capacity than a square grid withthe same cell area.

As indicated in FIG. 3, the beam pattern 28 wastes a large amount ofcapacity over the oceans. In FIG. 4, the cells over the ocean have beenexcluded from that of FIG. 3. This reduces the interference on operatingcells from cells over the ocean and reduces power consumed by thesatellite. It should be noted that tiling pattern 28′ in FIG. 4 does notmatch the boundaries of the countries. In a departure from typicalsatellite service planning, the present tiling pattern uses severalsmall beams to cover a country even when it is entirely accessible froma single orbit slot using a single beam. Coverage of a particularcountry may be constructed as a combination of all cells which touch itsterritory. Unless the country is too large to be entirely visible fromone orbit slot at a practical elevation angle, all of the beamsilluminating those cells could originate from a single orbit slot. If acountry chose to transmit the same programming to all of its cells, theycould use a single uplink signal which the satellite payload wouldtranslate to a different downlink frequency for each cell. The countrywould also have the flexibility to offer different programs in differentcells. This would require different signal switching within thesatellite payload. However, as long as the initial frequency planprovided adequate uplink bandwidth, there would be little or noregulatory impact to such a change in programming.

Referring now to FIG. 5, a histogram showing the number of cells fromFIG. 4 that can be utilized from the given number of orbit slots isillustrated. Two or more countries which share border cells may beserved from different orbit slots, so that each country has completecoverage. The number of cells which can be seen from the given number oforbit slots is computed using a minimum elevation angle of 20°, and aslot spacing of 6° over a range of −30° to +150° longitude. If thisnumber is less than the number of countries which the cell overlaps,then an orbit slot selection can be made that selects service to all ofthe countries overlapped. As is illustrated, a large number of cells areaccessible from 10 or more slots. For example, there are 170 cells thatmay be served by 20 orbit slots (beams) as shown by 33.

Referring now to FIG. 6, a wedge-shaped 60° sector of a tiling patternhaving a three-band reuse scheme 28 is shown with each cell 30 markedwith a letter which denotes a portion of the available spectrum thatdiffers from the others by frequency, polarization, or both. Inimplementation, the 60° sector illustrated would be extended six fold toencompass a circle centered around cell A₀. The other A frequencies,i.e., A₁₋₈, represent interference sources. The tiling pattern offrequency assignments is preferably continued across the applicablelandmasses of part of the entire visible Earth.

Referring now to FIG. 7, a tiling pattern 28 of cells 30 is shown havinga four-band reuse scheme. Only a 60° sector is illustrated as in FIG. 6.In this type of implementation, the interference between adjacent likefrequencies would be decreased due to the increased distance betweenlike cells.

Referring now to FIG. 8, a seven-band cell reuse scheme is establishedwithin tiling pattern 28. By using seven cells, interference is furtherreduced from the pattern shown in FIGS. 6 and 7 due to the increaseddistance between interference sources.

Provided that cells are sufficiently small, it has been calculated thatinterference over an area of a cell 30 is relatively constant. That is,because there are a large number of regularly distributed cell ringsover an area as the measurement is moved from one side of the cell tothe other, different cells become closer while others move further away.

If orbit slot spacing is large enough to provide adequate isolation,then a beam may be projected onto a cell from each orbit longitude.Isolation between beams from adjacent orbit slots is largely a functionof Earth-station antenna size and the associated side lobe gain. Forexample, in a three-band scheme such as that shown in FIG. 6, if oneorbit slot transmits the A channel set into a certain Earth-fixed cell,then the orbit slot 6° to the east, for example, may transmit frequencyB channel into that same cell. Similarly, B cells may switch to C and Cto A. If this scheme is followed, then a single cell may be fed from allaccessible orbit slots. The same is true for four-band frequency reuseand seven-band frequency reuse.

Referring now to FIG. 9, a plot of accessible GSO arc versus celllatitude plot is shown. Three lines are shown which define an elevationangle greater than 30°, greater than 20°, and greater than 10°. Thenumber of orbit slots which can serve a particular cell is proportionalto the length of the accessible arc. Therefore, the capacity availableto a given cell is approximately the number of channels per beam timesthe length of the accessible arc divided by the orbit slot spacing,which may be 6° nominally. This corresponds to antenna size.

The tiling pattern illustrated in FIGS. 3 and 4 use cells with 0.5° beamangles. The size 0.5° is somewhat arbitrarily chosen, however. In FIG.10, 2° beamwidth cells 30 are illustrated. As is shown, many fewer cellsare required to cover the landmasses. However, 2° cells may not enablereuse to achieve the desired high capacity overall.

Larger cells decrease spacecraft antenna size since the size of thebeams is reduced. Larger beams, however, cause orbit slot scarcity andcomplicate sharing of a spectrum between neighboring countries. Also,some capacity may be lost due to inefficient spectrum utilization.

In operation, the reference tiling pattern on the face of the Earthshould first be defined common to all satellites participating in thesystem. Because of power limits on satellites, more than a single setcan be implemented at each orbit location. The tiling pattern has anumber of cells associated with it. A plurality of beams are generatedfrom a first satellite. Each of the beams is directed to one of thecells. A second satellite in an adjacent slot generates a secondplurality of beams also direct. For a beam covering given cells, thesecond satellite should use a frequency band different from the firstsatellite. This alternation of bands from different slots of the presentinvention reduces interference between satellites and increases spectrumutilization. This scheme enables the coordination of coverage among allsatellites to achieve optimum capacity.

Thus, the relationships among the satellites of the present invention,including orbit slot spacing, common tiling patterns, and coordinatedfrequency reuse schemes, as well as antenna sizes and acceptedinterference levels enable a greatly increased utilization of theorbit/spectrum resource over that achieved by methods of coordinationused in the current state of the art.

While particular embodiments of the invention have been shown anddescribed, numerous variations and alternate embodiments will occur tothose skilled in the art. Accordingly, it is intended that the inventionbe limited only in terms of the appended claims.

1. A system of geostationary satellite orbits coordinatable with ageostationary belt of satellite positions having a plurality ofgeostationary slots, said system comprising: a plurality of satellitesforming a coordinatable system of geostationary satellite orbits thatprovides satellite coverage continuously within a specified servicearea; each satellite position being located in one of said plurality ofgeostationary slots and generating a plurality of beams in a respectivegroup of cells; and a fixed tiling pattern for use on the surface of theEarth, said tiling pattern having a plurality of cells corresponding tosaid plurality of beams, each of said cells having a defined frequencyfor communication and a frequency reuse spacing, wherein at least onebeam formed from a first of the plurality of satellites is directed toand coextensive with a group of cells formed from a second of theplurality of satellites so that at least one beam has a differentfrequency than each corresponding cell from the group of cells formedfrom the second of the plurality of satellites.
 2. A system as recitedin claim 1 further comprising a first satellite occupying a firstgeostationary slot generating a first set of uniform beams, and a secondsatellite occupying a second geostationary slot generating a second setof uniform beams.
 3. A system as recited in claim 2 wherein said firstset of beams and said second set of beams have a width of 0.5 degrees.4. A system as recited in claim 1 wherein said cells have an area thatis proportional to latitude on the surface of the Earth.
 5. A system asrecited in claim 1 wherein said tiling pattern is continuous.
 6. Asystem as recited in claim 1 wherein a tiling pattern first set ofparameters for forming a tiling pattern includes a reuse pattern.
 7. Asystem as recited in claim 1 wherein said tiling pattern comprises aplurality of hexagons.
 8. A satellite system as recited in claim 1wherein said first orbital slot and said second orbital slot arecoextensive.
 9. A satellite system as recited in claim 1 wherein thefirst satellite and the second satellite form a fixed satellite service.10. A satellite system as recited in claim 1 wherein the first satellitead the second satellite form a broadcast satellite service.
 11. Asatellite system as recited in claim 1 wherein a first subset beams ofthe plurality of beams sharing a same frequency band have asubstantially uniform signal power and a uniform C/(N+1) requirement,where C is an intended signal power, N is the noise power due to variousnatural thermal processes and I is a power due to all interferingsignals occupying the same frequency band as the intended signal.
 12. Asatellite system as recited in claim 1 wherein the tiling pattern formsregularly distributed cell rings.
 13. A satellite system as recited inclaim 1 wherein forming a tiling pattern comprises forming the tilingpattern from regularly distributed cell rings.
 14. A method of operatinga satellite system comprising the steps of: defining a fixed tilingpattern for use on the surface of the Earth having a number of cells;generating a first set of beams from a first satellite, each of thebeams directed to a first group of the cells; generating a second set ofbeams from a second satellite, each of the beams in said second set ofbeams directed to a second group of the cells, wherein at least one ofthe beams from the second set of beams is directed to and coextensivewith one in the first group of cells; and coordinating coverage fromsaid first set of beams and said second set of beams to avoidinterference between the first set of beams and the second set of beamsby assigning a frequency to the at least one of the beams from thesecond set of beams that has a different frequency than eachcorresponding cell formed from the first set of beams.
 15. A satellitesystem comprising: a plurality of orbit slots having a first orbit slotand a second orbit slot; a fixed tiling pattern for use on the surfaceof the Earth, said tiling pattern having a plurality of cells, each ofsaid cells having a defined frequency for communication; a firstsatellite occupying a first orbit slot generating a first set of beamsdirected to a first group of the plurality of cells; a second satelliteoccupying a second orbital slot generating a second set of beamsdirected to a second group of cells, wherein at least one of the beamsfrom the second set of beams is directed to and coextensive with one inthe first group of cells; and said first set of beams and said secondset of beams being generated according to predetermined parameters toavoid interference between said first set and said second set of beamsby assigning a frequency to the at least one of the beams from thesecond set of beams that has a different frequency than eachcorresponding cell formed from the first set of beams.